This invention relates to sanding blocks of the type having a surface adapted to have adhered thereto a piece of pressure-sensitive adhesive-coated finishing material (e.g., sandpaper) and a handle so that the sanding block can be manually manipulated to press and rub the finishing material against a surface to be finished. The prior art is replete with such sanding blocks. Known sanding blocks of this type, however, have only a planar surface to which the finishing material may be adhered. Thus while such sanding blocks provide proper support for rubbing finishing materials against planar surfaces, they do not facilitate finishing surfaces in radiused corners, grooves or openings in the workpiece being finished.